Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter B.3, Problem 6AYU
To test H0: σ = 0.35 versus H1: σ < 0.35, a random
- (a) If the sample standard deviation is determined to be s = 0.23, compute the test statistic.
- (b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, determine the critical value.
- (c) Draw a chi-square distribution and depict the critical region.
- (d) Will the researcher reject the null hypothesis? Why?
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Independent random samples selected from two normal populations produced the sample means and standard deviations shown to the right.
Assuming equal variances, conduct the test Ho: (uy - H2) = 0 against Ha: (H1 - H2) #0 using a = 0.10.
Sample 1 Sample 2
n, = 17
n2 = 13
%3D
x, = 5.3 x, = 7.6
S, = 3.9
S2 = 4.7
...
Find the test statistic.
The test statistic is
(Round to two decimal places as needed.)
Find the p-value.
The p-value is
(Round to three decimal places as needed.)
State the conclusion. Choose the correct answer below.
O A. Do not reject Ho. There is insufficient evidence that the means differ.
O B. Do not reject Ho. There is sufficient evidence that the means differ.
O C. Reject Ho. There is sufficient evidence that the means differ.
O D. Reject Ho. There is insufficient evidence that the means differ.
In a lake pollution study, the concentration of lead in the upper sedimentary layer of a lake bottom is
measured from 25 sediment samples. The sample mean and the standard deviation of the measurements
are found to be 0.38 and 0.06, respectively. Suppose
Ho : u = 0.34
H1: u# 0.34
(a) State Type I and Type Il errors.
(b) Conduct a hypothesis test at 0.01 level of significance by doing the seven-step classical approach.
(please show all seven steps, formulas, calculations and the curve)
To test Ho: o = 2.4 versus H₁: o>2.4, a random sample of size n=23 is obtained from a population that is known to be normally distributed.
(a) If the sample standard deviation is determined to be s= 3.3, compute the test statistic.
(b) If the researcher. decides to test this hypothesis at the x = 0.05 level of significance, use technology to determine the P-value.
(c) Will the researcher reject the null hypothesis?
(a) The test statistic is x² =.
A
(Round to two decimal places as needed.)
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Chapter B.3 Solutions
Fundamentals of Statistics (5th Edition)
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